Problema Solution
A small plane can fly 240 miles in 3 hours against the wind and can fly the same distance with the wind in 2 hours. What would e the total time for a round trip flight in still air?
Answer provided by our tutors
Let
v = the speed in still air
w = the speed of the wind
v + w = the speed with the wind
v - w = the speed against the wind
d = 240 mi the distance in each direction
t1 = 3 hr the time flying against the wind
t2 = 2 hr the time flying with the wind
Since distance = speed*time we have:
d = (v - w)*t1
(v - w)*3 = 240 divide both sides by 3
v - w = 80
d = (v + w)*t2
(v + w)*2 = 240 divide both sides by 2
v + w = 120
We have the following system of equations:
v - w = 80
v + w = 120
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click here to see the system of equations solved for v and w
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v = 100 mph
w = 10 mph
The time t for the round trip in still air is:
t = 2d/v
t = 2*240/100
t = 480/100
t = 4.8 hr
The total time for the round trip in still air is 4.8 hours.